The authors consider some aspects of accretion onto a rotating black hole immersed in a uniform magnetic field aligned with the angular momentum axis of the black hole. They specialise to motion in the equatorial plane, and calculate the 'Keplerian' angular momentum distribution and the marginally stable orbits. Using an unorthodox definition of the binding energy made necessary by an unphysical infinity induced by the assumed constancy of the magnetic field, they can calculate the marginally bound orbits and the efficiency of mass-to-energy conversion. When hydrodynamic accretion is considered the effects of the magnetic field are invariably quite small. For test particles, the magnetic field can significantly increase the efficiency, but this increase lessens as the specific angular momentum of the black hole rises.